Journal
Long-form notes, Qiskit experiments, and applied optimization thinking.
A step-by-step distinction between coherence, decoherence and wavefunction collapse. Starting from a single electron with no definite pre-measurement path, the note shows how interaction with an environment creates entanglement, why orthogonal environmental states suppress interference, why decoherence does not select one outcome, and why this leads to the quantum measurement problem.
Read note →A key conceptual obstacle in understanding coherence is the assumption that because there is only one electron, it must always occupy one definite position and follow one definite path. Quantum mechanics separates these ideas: there can be one electron while its quantum state does not assign it one definite position before measurement.
Read note →Beginning Chapter 3 with an intuitive understanding of vector spaces and subspaces: real components, R^2, closure under linear combinations, why y=2x forms a subspace but y=2x+1 does not, and how constraints reduce independent freedom.
Read note →Why does measuring which slit an electron passes through destroy interference? The answer is not human observation or the electron somehow noticing a detector. A physical interaction correlates the electron's paths with different detector states. The overlap between those detector states directly controls the surviving interference.
Read note →The double-slit experiment becomes genuinely quantum when electrons are sent one at a time. A spread of detector hits alone does not prove wave behavior; the crucial evidence is interference between probability amplitudes associated with alternative paths. This note follows the questions of what interferes, where negative phase comes from, whether one electron involves both paths, and what happens when we measure which slit it passes through.
Read note →A spread of electron impacts does not by itself demonstrate wave behavior. The important observation is that opening two possible paths produces a probability distribution that is not simply the sum of the distributions from each path separately. This note follows the learner's questions from localized electron detections to the real meaning of quantum interference.
Read note →A practical path through transpose and permutation matrices: why transpose is needed, how it connects rows and columns, why (AB)^T reverses order, why permutation matrices satisfy P^{-1}=P^T, and how left multiplication PA actually rearranges rows.
Read note →The familiar qubit equation |ψ⟩ = α|0⟩ + β|1⟩ was not invented as a standalone formula by one person. This note follows the question of where it came from, connecting classical wave superposition, Schrödinger's linear wave mechanics, Dirac's abstract state notation, and the later language of qubits.
Read note →Entanglement becomes much clearer when we stop treating it only as a factorization test and start asking what Alice and Bob actually observe when they measure. This note develops the Bell-state measurement behavior step by step, showing why same-basis measurements are perfectly correlated while different-basis measurements become 50/50.
Read note →Tensor products answer a basic question in quantum mechanics: how do we describe two quantum systems together? This note develops tensor products from scratch, shows why two qubits require a four-dimensional joint state space, and explains why a pure two-qubit state is entangled when it cannot be factored into separate pure states for Alice and Bob.
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